The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Zeitschrift für Analysis und ihre Anwendungen


Full-Text PDF (1307 KB) | Metadata | Table of Contents | ZAA summary
Volume 4, Issue 2, 1985, pp. 107–124
DOI: 10.4171/ZAA/141

Published online: 1985-04-30

Über das asymptotische Verhalten der Lösungen einer linearen Differentialgleichung mit Nachwirkung

Klaus Morgenthal[1]

(1) Humboldt-Universität zu Berlin, Germany

In the paper for the differential equation $$x’(t) = \int^\infty_{\tau=0} x(t-\tau) dr(t, \tau)$$ necessary conditions and sufficient conditions for the existence of eventually positive solutions are given which generalize known conditions. Their eventually positive solutions are estimated by means of solutions of the related differential inequalities. Finally an expansion theorem is proved. The results are mainly based on the consideration of the solutions of the differential inequalities and the application of comparison theorems for these solutions.

No keywords available for this article.

Morgenthal Klaus: Über das asymptotische Verhalten der Lösungen einer linearen Differentialgleichung mit Nachwirkung. Z. Anal. Anwend. 4 (1985), 107-124. doi: 10.4171/ZAA/141